There are any number of situations in which be can be deleted (or, alternatively, prevented from appearing) in subordinate -- and even main -- clauses.
A very simple example is Whiz-Deletion, which applies to restrictive relative clauses, and deletes (as I will call it) the subject relative pronoun (the "Wh-" part) plus whatever inflected form of be it agrees with (the "-iz" part), relating, for instance,
- The man who is standing on the corner is winking at me
- The man standing on the corner is winking at me,
thereby also relating most post-nominal phrasal modifiers to equivalent relative clauses.
Another is to be-Deletion, which applies to infinitive complement clauses, and is governed by the predicate, like the infinitive complementizer it modifies.
Verbs that allow to be-Deletion include declare, consider, and feel.
- He declared/considered/felt Max (to be) responsible for the accident. [optional to be]
Verbs that don't allow it include state, know, hear, and intend.
- He stated/knew/heard/intended Max to be responsible for the accident.
- *He stated/knew/heard/intended Max responsible for the accident. [obligatory to be]
A third rule, Conversational Deletion, applies only in main clauses, at the very beginning of a sentence. It deletes any predictable (i.e, meaningless, dummy, auxiliary, grammar particle, etc.) element, producing such normal utterances as
- Too bad about old Charlie. [from It is too bad]
- No need to get upset about it. [from There is no need]
Note that none of these delete copulas alone, but only as part of some complex, usually with a subject and/or other function word being deleted as well. There's no reason to delete a copula until it's not needed any more.